Switched capacitor circuits used for processing signals such as in ΣΔ converters typically sample the input to such a converter and then sum it with the similarly sampled feedback signal. The difference in the summed signals is typically amplified, filtered, and/or quantized to provide the feedback signal and an output to subsequent systems. Inherent in switched capacitor circuits is the problem of thermal switch noise which is defined as:       Noise    RMS    =            kT              C        sample            where T is the absolute temperature, Csample is the value of the capacitor and k is a physical constant. Thus it can be seen that to reduce the noise by a factor of 2 the capacitance must be increased by a factor of 4. A substantial reduction in noise would require a large increase in the size of the capacitance: usually this is not desirable. One of the primary limiting factors either in terms of the overall signal-to-noise ratio of the ΣΔ converter or in terms of the chip area is the size of the input sampling capacitor on the first integrator stage of the ΣΔ converter.
In ΣΔ converters oversampling is used in the quantizer and the oversampling rate (OSR) works to reduce the size of the capacitance to achieve a predetermined reduction in noise as expressed by the equation:       Noise    RMS    =            kT                        C          sample                ·        OSR            However, there is a limit to the OSR that can be applied, while the noise versus capacitance size problem persists. As can be seen from these expressions, the larger the input capacitor, the smaller the thermal noise stored on the capacitor due to the input switches. For very high-performance circuits with high signal-to-noise ratios, the size of the input sampling capacitor gets prohibitively large. Correspondingly, the complexity and power consumption of the driving amplifier increases as does the size of the sampling switches. The issue of “kT/C” noise (as the wide-band thermal noise is more popularly known) is valid in any sampled system using switches and capacitors and ΣΔ modulator A/D converters are only a subset.